Internal 'customers' are said to be the people in your company or perhaps a partner that you provide your services too in order to deliver your company's products or services. External customers are said to be those people that actually buy your company's products or services. These are certainly cute and clever definitions.
But let's clear the fog - there is only one "customer" - the people that actually buy products and services from your company and which your company derives revenues!
When I hear "Run IT like a Business" I can't help but cringe. It has way too much room for interpretation, and given the creative minds that are in IT, just about every interpretation has been tried. We really do not want to run IT like a business, rather 'run IT with business discipline' is probably a more appropriate phrasing.
Why don't we want to run IT like a business? There are many reasons - the first being does your business really want/need IT to be run like a business? After all, business is run for profit with targeted margins and there are marketing activities to drive revenue. Those alone are big enough reasons your company probably doesn't really want to run IT like a business, but does want it run with responsible business discipline and practices.
But even more dangerously, I've seen many company's IT organizations talking about their 'customer', meaning internal customers. This way of thinking and worse, operating, causes many undue problems and unproductive activities. Situations stemming from statements such as 'the customer is always right' is a common one in addition to very wasteful pampering.
Anyone that you work with in the overall delivery (e.g. design, development, manufacturing, distribution, marketing, sale, etc.) of a product or service that the company sells, is a co-worker. Whether they be an actual employee, contractor, or partner. And as such the mission and focus should be on the customer that buys the products or services. Co-workers should treat each other with professional respect, courtesy, and do so in a pleasant and productive manner.
Alignment happens at the customer
By each organization within the company focused on the real customer and actually working together toward that end and not spending cycles trying to 'satisfy' each other through fictitious role playing, every part of the organization will bring its best to the process and all parts of the company will naturally begin to align.
This 'our customer' view is as much, if not more, an ideology change as an operational change, and doing it will yield many productive benefits.